I have an irrational affinity for claiming land on the map. Civilization IV and V expand your empire’s borders through culture, somewhat like Zerg creep except that it just keeps going. Civ V took away the dueling culture aspect, whereby empire borders would fluctuate as one culture overpowered another on a tile. This makes the Great Artist’s culture bomb much less impressive, although more permanent; it also takes away the immensely satisfying culture conquest of cities, whereby cities in other nations riot and defect because you are just that awesome.
Expanding your cultural borders is an effective defense. The further away enemy units must stay without either your permission or a declaration of war, the more time you have to marshal your defenses when that war happens. It also lets you claim some nice tiles beyond your cities’ borders, because whether or not you can use them, you do not want anyone else to have them. You can also block major travel routes so that those not in your favor must go decades out of their way.
I’m sure this is some primal mammalian urge, the digital equivalent of peeing on trees to mark your territory. It is still enormously gratifying to see the entire continent in your color while the numbers on the meters at the top of the screen keep going up.